{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2020:WRY5IPTWECTZ4T5B3ULZFR2PE4","short_pith_number":"pith:WRY5IPTW","schema_version":"1.0","canonical_sha256":"b471d43e7620a79e4fa1dd1792c74f27267ffe2982c026d7f174753c49dc614e","source":{"kind":"arxiv","id":"2007.11767","version":1},"attestation_state":"computed","paper":{"title":"Non-trivial $t$-intersecting families for vector spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Benjian Lv, Kaishun Wang, Mengyu Cao, Sanming Zhou","submitted_at":"2020-07-23T03:14:30Z","abstract_excerpt":"Let $V$ be an $n$-dimensional vector space over a finite field $\\mathbb{F}_q$. In this paper we describe the structure of maximal non-trivial $t$-intersecting families of $k$-dimensional subspaces of $V$ with large size. We also determine the non-trivial $t$-intersecting families with maximum size. In the special case when $t=1$ our result gives rise to the well-known Hilton-Milner Theorem for vector spaces."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2007.11767","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2020-07-23T03:14:30Z","cross_cats_sorted":[],"title_canon_sha256":"e27f108a08bdf3ca9d3c1a390a49ec434d7872ac1c6bb96925b1f84bd42443a9","abstract_canon_sha256":"afd32d03d4f0577e3c475af9f34bfcdfce57999f5936dbcec158f43e03ddcea5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:21:40.181856Z","signature_b64":"IzwW87kx0FO6lQXJ2LAcrccNpqybEKgRPOn7I0P1MRMPyzroxpDobU7Fs0wspZMvg2u6voTpotWoCb8Og0EsDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b471d43e7620a79e4fa1dd1792c74f27267ffe2982c026d7f174753c49dc614e","last_reissued_at":"2026-07-05T01:21:40.181448Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:21:40.181448Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Non-trivial $t$-intersecting families for vector spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Benjian Lv, Kaishun Wang, Mengyu Cao, Sanming Zhou","submitted_at":"2020-07-23T03:14:30Z","abstract_excerpt":"Let $V$ be an $n$-dimensional vector space over a finite field $\\mathbb{F}_q$. In this paper we describe the structure of maximal non-trivial $t$-intersecting families of $k$-dimensional subspaces of $V$ with large size. We also determine the non-trivial $t$-intersecting families with maximum size. In the special case when $t=1$ our result gives rise to the well-known Hilton-Milner Theorem for vector spaces."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2007.11767","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2007.11767/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2007.11767","created_at":"2026-07-05T01:21:40.181506+00:00"},{"alias_kind":"arxiv_version","alias_value":"2007.11767v1","created_at":"2026-07-05T01:21:40.181506+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2007.11767","created_at":"2026-07-05T01:21:40.181506+00:00"},{"alias_kind":"pith_short_12","alias_value":"WRY5IPTWECTZ","created_at":"2026-07-05T01:21:40.181506+00:00"},{"alias_kind":"pith_short_16","alias_value":"WRY5IPTWECTZ4T5B","created_at":"2026-07-05T01:21:40.181506+00:00"},{"alias_kind":"pith_short_8","alias_value":"WRY5IPTW","created_at":"2026-07-05T01:21:40.181506+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/WRY5IPTWECTZ4T5B3ULZFR2PE4","json":"https://pith.science/pith/WRY5IPTWECTZ4T5B3ULZFR2PE4.json","graph_json":"https://pith.science/api/pith-number/WRY5IPTWECTZ4T5B3ULZFR2PE4/graph.json","events_json":"https://pith.science/api/pith-number/WRY5IPTWECTZ4T5B3ULZFR2PE4/events.json","paper":"https://pith.science/paper/WRY5IPTW"},"agent_actions":{"view_html":"https://pith.science/pith/WRY5IPTWECTZ4T5B3ULZFR2PE4","download_json":"https://pith.science/pith/WRY5IPTWECTZ4T5B3ULZFR2PE4.json","view_paper":"https://pith.science/paper/WRY5IPTW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2007.11767&json=true","fetch_graph":"https://pith.science/api/pith-number/WRY5IPTWECTZ4T5B3ULZFR2PE4/graph.json","fetch_events":"https://pith.science/api/pith-number/WRY5IPTWECTZ4T5B3ULZFR2PE4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WRY5IPTWECTZ4T5B3ULZFR2PE4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WRY5IPTWECTZ4T5B3ULZFR2PE4/action/storage_attestation","attest_author":"https://pith.science/pith/WRY5IPTWECTZ4T5B3ULZFR2PE4/action/author_attestation","sign_citation":"https://pith.science/pith/WRY5IPTWECTZ4T5B3ULZFR2PE4/action/citation_signature","submit_replication":"https://pith.science/pith/WRY5IPTWECTZ4T5B3ULZFR2PE4/action/replication_record"}},"created_at":"2026-07-05T01:21:40.181506+00:00","updated_at":"2026-07-05T01:21:40.181506+00:00"}